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Well-posedness of fully nonlinear and nonlocal critical parabolic equations

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Abstract

In this paper, we prove the existence of smooth solutions in Sobolev spaces to fully nonlinear and nonlocal parabolic equations with critical index. Our argument is to transform the fully nonlinear equation into a quasi-linear nonlocal parabolic equation.

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  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, People’s Republic of China

    Xicheng Zhang

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  1. Xicheng Zhang
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Correspondence to Xicheng Zhang.

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Zhang, X. Well-posedness of fully nonlinear and nonlocal critical parabolic equations. J. Evol. Equ. 13, 135–162 (2013). https://doi.org/10.1007/s00028-012-0172-0

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  • DOI: https://doi.org/10.1007/s00028-012-0172-0

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